Poverty is measured in two steps: decide who counts as poor, then summarise how much poverty there is. Six measures cover everything the papers ask, and each one fits on a card: its name, symbol, formula and a plain explanation.
01
Start here
Two jobs: draw the line, then summarise
Job 1
Who is poor?
Pick a poverty line and call everyone below it poor. The line can be a fixed basket of needs (absolute) or a fraction of what a typical person earns (relative).
Job 2
How much poverty is there?
Squash the incomes of the poor into one number. It can ignore their depth (H), average it (PG), stress the worst off (P₂), or count deprivations instead of rupees (MPI).
npeople in the population
qpeople below the line (the poor)
yiincome (or spending) of person i
zthe poverty line
zz−yiperson i's gap: how far below the line, as a share of the line
02
Job 1
Drawing the line: absolute and relative
Absolute poverty line
z
yi<z,z=cost of a basket of basic needs
What it is
A fixed amount of spending (or income) per person, chosen to buy a minimum basket of food and other necessities. Below it you are poor; above it you are not.
How it works
The line is set in real terms, so it does not move with the rest of society: if everyone gets richer, the count of poor falls.
Worth knowing
India's official line is absolute and consumption-based; the World Bank's international line is the same idea in dollars a day.
India Official 2011–12 (Tendulkar): ₹816 rural, ₹1,000 urban a month. World Bank line: $3.00 a day (2021 PPP).
Relative poverty line
z = k·m
z=k×m,m=median income,k≈0.5 to 0.6
What it is
A line tied to the rest of society: you are poor if you earn well below what a typical person earns, usually half or 60% of the median.
How it works
Because the line moves with the median, it measures being left behind, not being unable to buy a basket of goods.
Worth knowing
If every income doubles, relative poverty does not change at all, so it behaves like an inequality measure. The EU uses 60% of the median.
India No official relative line. World Bank societal poverty line (partly relative): $4.07 a day in 2022; 21.3% below it.
The difference in one sentence
An absolute line asks “can you afford the basket?”; a relative line asks “are you far behind everyone else?”. Double every income and absolute poverty falls; relative poverty stays exactly where it was.
03
Job 2
Summarising poverty: H, PG and P₂
Once there is a line, three numbers summarise poverty. They are one formula with a dial, α, that sets how heavily the poorest are weighted.
The Foster–Greer–Thorbecke family
Pα=n1i=1∑q(zz−yi)α
α = 0 gives the headcount ratio H; α = 1 the poverty gap index PG; α = 2 the squared poverty gap P₂. The income-gap ratio, the average shortfall of the poor alone, is I=PG/H.
Headcount ratio
H
H=nq
What it is
The share of the population below the poverty line: q poor people out of n people in all.
How it works
It is the number everyone quotes ("21.9% poor"), and the easiest to compute: count heads, divide.
Worth knowing
It ignores how poor the poor are. A person who is poor and becomes poorer leaves H unchanged; a poor person who moves from just below the line to just above it lowers H by a lot.
India 5.3% at $3.00 a day (2022–23). Official 21.9% (2011–12, Tendulkar).
Poverty gap index
PG
PG=n1i=1∑qzz−yi
What it is
How far below the line the poor are, on average, as a share of the line, with the non-poor counted as zero.
How it works
Each poor person's shortfall z − yᵢ is divided by z, added up and divided by everyone, n. Multiplied by n × z, it is the total cost of lifting every poor person exactly to the line.
Worth knowing
Unlike H, it falls when a poor person's income rises even if they stay below the line. It does not care how the shortfall is spread among the poor.
India 0.8% at $3.00 a day (2022–23).
Squared poverty gap
P₂
P2=n1i=1∑q(zz−yi)2
What it is
The poverty gap with each shortfall squared first, so the poorest count for much more.
How it works
A poor person twice as far below the line adds four times as much. It measures the severity of poverty, not just its depth.
Worth knowing
It is the only one of the three that falls when income is transferred from a richer poor person to a poorer one. H and PG do not notice.
India 0.2% at $3.00 a day (2022–23).
Which measure notices which change? (✓ = it changes, — = it does not)
What happens
H
PG
P₂
A poor person gets poorer, and stays poor
—
✓
✓
A poor person crosses the line
✓
✓
✓
Income moves from a richer poor person to a poorer one
—
—
✓
04
Beyond income
Beyond income: the MPI
Multidimensional Poverty Index
MPI
MPI=H×A
What it is
Counts deprivations rather than rupees: a household is poor if it is deprived in at least a third of the weighted indicators across health, education and living standards.
How it works
H is the share of people who are poor in this sense; A, the intensity, is the average share of indicators in which the poor are deprived. Multiply them.
Worth knowing
Being a product, it falls if fewer people are poor or if the poor are deprived in fewer ways. India's national MPI uses 12 indicators; the global one uses 10.
India National MPI (NITI Aayog) 0.066 in 2019–21, with 14.96% poor, down from 24.85% in 2015–16.
05
Interactive
Try it
Type up to twelve incomes and move the line z. Watch H jump when someone crosses it, PG move smoothly, and P₂ react most to the very poorest.
z = 50
20406080100
Poor: income below zShortfall z − yNot poor
2 of 5 people are poor, so the headcount is 0.4. It ignores how poor they are: lift the poorest person by a little and it does not move. The poverty gap does move, and the squared gap moves most when the gain goes to the very poorest.
Worked example · poverty gap index
Four people earn 200, 220, 300 and 320. The poverty line is 250. Find the poverty gap index.
1
The poor.
200 and 220 are below 250, so q = 2.
2
Their gaps.
25050=0.2,25030=0.12
3
Average over everyone.
PG=40.2+0.12=0.08
Answer
PG = 0.08 (and H = 0.5)
06
Exam traps
Exam traps
Watch out for
The mistakes examiners are fishing for
Divide by n, not q. H, PG and P₂ all average over the whole population. Divide the gaps by q and you get the income-gap ratio instead.
Headcount ignores depth. Making a poor person poorer does not change H; it raises PG and P₂.
Poor means strictly below z. Someone exactly on the line is not poor.
Relative poverty is scale-free. Multiply every income by 2 and a relative line moves with them, so nothing changes.
MPI is H × A. A is the intensity among the poor, not among everyone.
PG is not the poverty gap in rupees. It is a share of z. Multiply by n × z to get the total shortfall.
07
Practice
Check yourself
0 of 10 correct so far
A. Numbers
Problem 1
Incomes are 100, 120, 140 and 155; the poverty line is 150. Find the headcount ratio and the poverty gap index.
Problem 2
Incomes are 20, 50, 80 and 120; the poverty line is 100. Find H, PG and the squared poverty gap P₂.
B. Concepts
1If a poor person becomes poorer but stays poor, which measure is unchanged?
2Which measure falls when income is transferred from a richer poor person to a poorer poor person, with both still below the line?
3A relative poverty line is set at half the median income. If every income doubles, relative poverty:
4In a multidimensional poverty index, H = 40% of people are poor and they are deprived in 50% of the weighted indicators on average. The MPI is:
5The Foster–Greer–Thorbecke measure with α = 0 is:
Foster, Greer and Thorbecke (1984), 'A Class of Decomposable Poverty Measures', Econometrica 52(3)
Alkire and Foster (2011), 'Counting and Multidimensional Poverty Measurement', Journal of Public Economics 95
Datt & Sundharam's Indian Economy (S. Chand, 2020): 'Poverty and the Planning Process in India'
The small grey “India” lines are for context only; the exams ask the definitions and the arithmetic.
Try it on real questions
Seven past-paper questions on poverty measures
From the University of Hyderabad, JNU, CUET-PG, UGC NET and IIT JAM: computing the headcount ratio and the poverty gap, the poverty line and the MPI.
✦These are questions from the TestStop bank. A free account answers 10 a day, each with its worked solution; All-Access opens every set with no daily limit.
